Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing
Abstract
We study descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds. We use the wall-crossing setup developed by the author and Joyce in Joyce's Lie algebra H*(Npl,Q) of the projective-linear pairs stack, and next pass to Gross's polynomial realization eκQ[sjkℓ]. We compute explicit examples of one-dimensional Donaldson--Thomas invariants on Fano 3-folds and, via wall-crossing, Pandharipande--Thomas stable pair invariants and descendent generating series. We compute examples on PP3, on a smooth cubic threefold, on BlpPP3, on BlℓPP3, and on the projective-bundle threefold PP(OOX⊕ OOX(−1,−1)) over X=PP1×PP1. In the PP3 and cubic threefold examples we compare the intrinsic large-n tails with the formulas of Pandharipande and Moreira and show that, in the cases treated in common, the differences are Laurent polynomials.
Versions
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BibTeX
@misc{anderson2026examples,
title = {{Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing}},
author = {Reginald Anderson},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2607.02526},
eprint = {2607.02526},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2607.02526},
note = {CC BY-NC-ND 4.0},
}
RIS
TY - UNPB
TI - Examples of descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds via one-dimensional wall-crossing
AU - Reginald Anderson
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2607.02526
UR - https://arxiv.org/abs/2607.02526
AB - We study descendent generating series for Pandharipande--Thomas stable pairs on smooth projective Fano threefolds. We use the wall-crossing setup developed by the author and Joyce in Joyce's Lie algebra H_*(N^pl,Q) of the projective-linear pairs stack, and next pass to Gross's polynomial realization e^κQ[s_jkℓ]. We compute explicit examples of one-dimensional Donaldson--Thomas invariants on Fano 3-folds and, via wall-crossing, Pandharipande--Thomas stable pair invariants and descendent generating series. We compute examples on PP^3, on a smooth cubic threefold, on Bl_pPP^3, on Bl_ℓPP^3, and on the projective-bundle threefold PP(OO_X⊕ OO_X(−1,−1)) over X=PP^1×PP^1. In the PP^3 and cubic threefold examples we compare the intrinsic large-n tails with the formulas of Pandharipande and Moreira and show that, in the cases treated in common, the differences are Laurent polynomials.
ER -